How to calculate diameter from circumference

A circumference is the distance around any closed curve; it is also a special type of perimeter. However, it generally refers to the circumference of a circle unless otherwise specified. The term "circumference" also may refer to the length of this distance. A diameter of a circle is a line segment that intersects the centre of a circle with its endpoints on the circle. You can calculate the length of a circle's diameter if you know its circumference.

Learn the significance of pi--a value that is defined as the ratio of a circle's circumference to its diameter. This means that pi = c/d where c is the circumference and d is its diameter. Therefore, the equation d = c/(pi) gives you the diameter of a circle when you know its circumference.

Know how to express the value of pi for a particular problem. The value of pi rounded to six decimal places is 3.141593, but the exact value of pi can never be known because its expression as a decimal value does not end nor does it repeat. Therefore, any literal value of pi will always be an estimate. You may simply leave it in the solution as "pi" for some problems; for other problems, you may need to provide an approximate value of pi that is accurate to the desired number of decimal places.

Solve for the diameter when the circumference is a multiple of pi. If the circumference is 4(pi), then d = c/(pi) = 4(pi)/(pi) = 4 using the formula in Step 1.

Solve for the diameter with an approximation of pi. If the circumference is 12, you know the diameter is d = c/(pi) = 12/(pi). You can estimate the diameter to two decimal places as d = 12/3.142 = 3.82. Note that using a value of pi that is accurate to three decimal places in your calculation ensures two decimal places of accuracy in the final answer. This eliminates the possibility of round-off error in the second decimal place of the final answer.

Things You'll Need

  • Calculator
Cite this Article A tool to create a citation to reference this article Cite this Article

About the Author

Allan Robinson has written numerous articles for various health and fitness sites. Robinson also has 15 years of experience as a software engineer and has extensive accreditation in software engineering. He holds a bachelor's degree with majors in biology and mathematics.